Problem: $-6de + 4e + 7f - 7 = 2e + 2f - 9$ Solve for $d$.
Combine constant terms on the right. $-6de + 4e + 7f - {7} = 2e + 2f - {9}$ $-6de + 4e + 7f = 2e + 2f - {2}$ Combine $f$ terms on the right. $-6de + 4e + {7f} = 2e + {2f} - 2$ $-6de + 4e = 2e - {5f} - 2$ Combine $e$ terms on the right. $-6de + {4e} = {2e} - 5f - 2$ $-6de = -{2e} - 5f - 2$ Isolate $d$ $-{6}d{e} = -2e - 5f - 2$ $d = \dfrac{ -2e - 5f - 2 }{ -{6e} }$ Swap the signs so the denominator isn't negative. $d = \dfrac{ {2}e + {5}f + {2} }{ {6e} }$